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Trevor Wilson
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Definable Wellordering of the Reals

Why are we interested in definable wellordering of the reals? For instance, we have

  1. Con(ZFC) $\Rightarrow$ Con(ZFC + there is a $\Delta^1_2$-wellordering of $\mathbb{R}$),
  2. Con(ZFC + there is a measurable cardinal) $\Rightarrow$ Con(ZFC + there is a measurable cardinal+there is a $\Delta^1_3$-wellordering of $\mathbb{R}$).